Headshot, even with a 22lr. Too much meat damage from any of those calibers. I've gone over to the dark side with the 17hmr, (just too much fun shooting it.) The only round I used that didn't ruin the meat was a .22lr lead round nose target round.
A few folks hereabouts need to learn to place their shot to avoid meat damage. I've hunted small game with a handgun, as well as a rifle with nearly no meat damaage at all.
Head shots are the norm, but a chest hit through the ribs with a subsonic .22 LR works great. I prefer the Rem subsonics, but mostly because they're easy to find here...and are cheap.
It isn't rocket science; just put the bullet where the meat isn't, and avoid gut shooting them in order to avoid tainting the meat.
The .22 LR has been taking small game for more decades than any of us can count, and it'll continue to do so. It's what it was designed for, and it does the job well.